arXiv subjects

Karl Tuyls

Publications and source records attributed to Karl Tuyls.

At least 19 recordsLinked to original sources

arXiv2024

An Analysis of Quantile Temporal-Difference Learning

We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these empirical successes, a theoretical understanding of QTD has proven elusive until now. Unlike classical TD learning, which can be analysed with standard stochastic approximation tools, QTD updates do not approximate contraction mappings, are highly non-linear, and may have multiple fixed points. The core result of this paper is a proof of convergence to the fixed points of a related family of dynamic programming procedures with probability 1, putting QTD on firm theoretical footing. The proof establishes connections between QTD and non-linear differential inclusions through stochastic approximation theory and non-smooth analysis.

cs.LG↗

arXiv2024

Using deep reinforcement learning to promote sustainable human behaviour on a common pool resource problem

A canonical social dilemma arises when finite resources are allocated to a group of people, who can choose to either reciprocate with interest, or keep the proceeds for themselves. What resource allocation mechanisms will encourage levels of reciprocation that sustain the commons? Here, in an iterated multiplayer trust game, we use deep reinforcement learning (RL) to design an allocation mechanism that endogenously promotes sustainable contributions from human participants to a common pool resource. We first trained neural networks to behave like human players, creating a stimulated economy that allowed us to study how different mechanisms influenced the dynamics of receipt and reciprocation. We then used RL to train a social planner to maximise aggregate return to players. The social planner discovered a redistributive policy that led to a large surplus and an inclusive economy, in which players made roughly equal gains. The RL agent increased human surplus over baseline mechanisms based on unrestricted welfare or conditional cooperation, by conditioning its generosity on available resources and temporarily sanctioning defectors by allocating fewer resources to them. Examining the AI policy allowed us to develop an explainable mechanism that performed similarly and was more popular among players. Deep reinforcement learning can be used to discover mechanisms that promote sustainable human behaviour.

cs.AI↗

arXiv2024

Multi-Agent Training beyond Zero-Sum with Correlated Equilibrium Meta-Solvers

Two-player, constant-sum games are well studied in the literature, but there has been limited progress outside of this setting. We propose Joint Policy-Space Response Oracles (JPSRO), an algorithm for training agents in n-player, general-sum extensive form games, which provably converges to an equilibrium. We further suggest correlated equilibria (CE) as promising meta-solvers, and propose a novel solution concept Maximum Gini Correlated Equilibrium (MGCE), a principled and computationally efficient family of solutions for solving the correlated equilibrium selection problem. We conduct several experiments using CE meta-solvers for JPSRO and demonstrate convergence on n-player, general-sum games.

cs.MA↗

arXiv2024

Empirical Game-Theoretic Analysis: A Survey

In the empirical approach to game-theoretic analysis (EGTA), the model of the game comes not from declarative representation, but is derived by interrogation of a procedural description of the game environment. The motivation for developing this approach was to enable game-theoretic reasoning about strategic situations too complex for analytic specification and solution. Since its introduction over twenty years ago, EGTA has been applied to a wide range of multiagent domains, from auctions and markets to recreational games to cyber-security. We survey the extensive methodology developed for EGTA over the years, organized by the elemental subproblems comprising the EGTA process. We describe key EGTA concepts and techniques, and the questions at the frontier of EGTA research. Recent advances in machine learning have accelerated progress in EGTA, and promise to significantly expand our capacities for reasoning about complex game situations.

cs.GT↗

arXiv2024

Towards a Pretrained Model for Restless Bandits via Multi-arm Generalization

Restless multi-arm bandits (RMABs), a class of resource allocation problems with broad application in areas such as healthcare, online advertising, and anti-poaching, have recently been studied from a multi-agent reinforcement learning perspective. Prior RMAB research suffers from several limitations, e.g., it fails to adequately address continuous states, and requires retraining from scratch when arms opt-in and opt-out over time, a common challenge in many real world applications. We address these limitations by developing a neural network-based pre-trained model (PreFeRMAB) that has general zero-shot ability on a wide range of previously unseen RMABs, and which can be fine-tuned on specific instances in a more sample-efficient way than retraining from scratch. Our model also accommodates general multi-action settings and discrete or continuous state spaces. To enable fast generalization, we learn a novel single policy network model that utilizes feature information and employs a training procedure in which arms opt-in and out over time. We derive a new update rule for a crucial $λ$-network with theoretical convergence guarantees and empirically demonstrate the advantages of our approach on several challenging, real-world inspired problems.

cs.LG↗

arXiv2024

Steering Language Models with Game-Theoretic Solvers

Mathematical models of interactions among rational agents have long been studied in game theory. However these interactions are often over a small set of discrete game actions which is very different from how humans communicate in natural language. To bridge this gap, we introduce a framework that allows equilibrium solvers to work over the space of natural language dialogue generated by large language models (LLMs). Specifically, by modelling the players, strategies and payoffs in a "game" of dialogue, we create a binding from natural language interactions to the conventional symbolic logic of game theory. Given this binding, we can ask existing game-theoretic algorithms to provide us with strategic solutions (e.g., what string an LLM should generate to maximize payoff in the face of strategic partners or opponents), giving us predictors of stable, rational conversational strategies. We focus on three domains that require different negotiation strategies: scheduling meetings, trading fruit and debate, and evaluate an LLM's generated language when guided by solvers. We see that LLMs that follow game-theory solvers result in dialogue generations that are less exploitable than the control (no guidance from solvers), and the language generated results in higher rewards, in all negotiation domains. We discuss future implications of this work, and how game-theoretic solvers that can leverage the expressivity of natural language can open up a new avenue of guiding language research.

cs.CL↗

arXiv2023

TacticAI: an AI assistant for football tactics

Identifying key patterns of tactics implemented by rival teams, and developing effective responses, lies at the heart of modern football. However, doing so algorithmically remains an open research challenge. To address this unmet need, we propose TacticAI, an AI football tactics assistant developed and evaluated in close collaboration with domain experts from Liverpool FC. We focus on analysing corner kicks, as they offer coaches the most direct opportunities for interventions and improvements. TacticAI incorporates both a predictive and a generative component, allowing the coaches to effectively sample and explore alternative player setups for each corner kick routine and to select those with the highest predicted likelihood of success. We validate TacticAI on a number of relevant benchmark tasks: predicting receivers and shot attempts and recommending player position adjustments. The utility of TacticAI is validated by a qualitative study conducted with football domain experts at Liverpool FC. We show that TacticAI's model suggestions are not only indistinguishable from real tactics, but also favoured over existing tactics 90% of the time, and that TacticAI offers an effective corner kick retrieval system. TacticAI achieves these results despite the limited availability of gold-standard data, achieving data efficiency through geometric deep learning.

cs.LG↗

arXiv2023

Heterogeneous Social Value Orientation Leads to Meaningful Diversity in Sequential Social Dilemmas

In social psychology, Social Value Orientation (SVO) describes an individual's propensity to allocate resources between themself and others. In reinforcement learning, SVO has been instantiated as an intrinsic motivation that remaps an agent's rewards based on particular target distributions of group reward. Prior studies show that groups of agents endowed with heterogeneous SVO learn diverse policies in settings that resemble the incentive structure of Prisoner's dilemma. Our work extends this body of results and demonstrates that (1) heterogeneous SVO leads to meaningfully diverse policies across a range of incentive structures in sequential social dilemmas, as measured by task-specific diversity metrics; and (2) learning a best response to such policy diversity leads to better zero-shot generalization in some situations. We show that these best-response agents learn policies that are conditioned on their co-players, which we posit is the reason for improved zero-shot generalization results.

cs.MA↗

arXiv2023

Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers

Solution concepts such as Nash Equilibria, Correlated Equilibria, and Coarse Correlated Equilibria are useful components for many multiagent machine learning algorithms. Unfortunately, solving a normal-form game could take prohibitive or non-deterministic time to converge, and could fail. We introduce the Neural Equilibrium Solver which utilizes a special equivariant neural network architecture to approximately solve the space of all games of fixed shape, buying speed and determinism. We define a flexible equilibrium selection framework, that is capable of uniquely selecting an equilibrium that minimizes relative entropy, or maximizes welfare. The network is trained without needing to generate any supervised training data. We show remarkable zero-shot generalization to larger games. We argue that such a network is a powerful component for many possible multiagent algorithms.

cs.LG↗

arXiv2023

Human-Timescale Adaptation in an Open-Ended Task Space

Foundation models have shown impressive adaptation and scalability in supervised and self-supervised learning problems, but so far these successes have not fully translated to reinforcement learning (RL). In this work, we demonstrate that training an RL agent at scale leads to a general in-context learning algorithm that can adapt to open-ended novel embodied 3D problems as quickly as humans. In a vast space of held-out environment dynamics, our adaptive agent (AdA) displays on-the-fly hypothesis-driven exploration, efficient exploitation of acquired knowledge, and can successfully be prompted with first-person demonstrations. Adaptation emerges from three ingredients: (1) meta-reinforcement learning across a vast, smooth and diverse task distribution, (2) a policy parameterised as a large-scale attention-based memory architecture, and (3) an effective automated curriculum that prioritises tasks at the frontier of an agent's capabilities. We demonstrate characteristic scaling laws with respect to network size, memory length, and richness of the training task distribution. We believe our results lay the foundation for increasingly general and adaptive RL agents that perform well across ever-larger open-ended domains.

cs.LG↗

arXiv2022

Game Theoretic Rating in N-player general-sum games with Equilibria

Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies have been used to rate strategies (e.g. Elo), however recent work has expanded ratings to utilize game theoretic solutions to better rate strategies in non-transitive games. This work generalizes these ideas and proposes novel algorithms suitable for N-player, general-sum rating of strategies in normal-form games according to the payoff rating system. This enables well-established solution concepts, such as equilibria, to be leveraged to efficiently rate strategies in games with complex strategic interactions, which arise in multiagent training and real-world interactions between many agents. We empirically validate our methods on real world normal-form data (Premier League) and multiagent reinforcement learning agent evaluation.

cs.GT↗

arXiv2022

Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environments

The Game Theory & Multi-Agent team at DeepMind studies several aspects of multi-agent learning ranging from computing approximations to fundamental concepts in game theory to simulating social dilemmas in rich spatial environments and training 3-d humanoids in difficult team coordination tasks. A signature aim of our group is to use the resources and expertise made available to us at DeepMind in deep reinforcement learning to explore multi-agent systems in complex environments and use these benchmarks to advance our understanding. Here, we summarise the recent work of our team and present a taxonomy that we feel highlights many important open challenges in multi-agent research.

cs.MA↗

arXiv2022

Learning Equilibria in Mean-Field Games: Introducing Mean-Field PSRO

Recent advances in multiagent learning have seen the introduction ofa family of algorithms that revolve around the population-based trainingmethod PSRO, showing convergence to Nash, correlated and coarse corre-lated equilibria. Notably, when the number of agents increases, learningbest-responses becomes exponentially more difficult, and as such ham-pers PSRO training methods. The paradigm of mean-field games pro-vides an asymptotic solution to this problem when the considered gamesare anonymous-symmetric. Unfortunately, the mean-field approximationintroduces non-linearities which prevent a straightforward adaptation ofPSRO. Building upon optimization and adversarial regret minimization,this paper sidesteps this issue and introduces mean-field PSRO, an adap-tation of PSRO which learns Nash, coarse correlated and correlated equi-libria in mean-field games. The key is to replace the exact distributioncomputation step by newly-defined mean-field no-adversarial-regret learn-ers, or by black-box optimization. We compare the asymptotic complexityof the approach to standard PSRO, greatly improve empirical bandit con-vergence speed by compressing temporal mixture weights, and ensure itis theoretically robust to payoff noise. Finally, we illustrate the speed andaccuracy of mean-field PSRO on several mean-field games, demonstratingconvergence to strong and weak equilibria.

cs.GT↗

arXiv2022

Learning Correlated Equilibria in Mean-Field Games

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game theoretic analysis becomes effectively infeasible beyond a low number of players. Recent approaches have gone around this limitation by instead considering Mean-Field games, an approximation of anonymous $N$-player games, where the number of players is infinite and the population's state distribution, instead of every individual player's state, is the object of interest. The practical computability of Mean-Field Nash equilibria, the most studied Mean-Field equilibrium to date, however, typically depends on beneficial non-generic structural properties such as monotonicity or contraction properties, which are required for known algorithms to converge. In this work, we provide an alternative route for studying Mean-Field games, by developing the concepts of Mean-Field correlated and coarse-correlated equilibria. We show that they can be efficiently learnt in \emph{all games}, without requiring any additional assumption on the structure of the game, using three classical algorithms. Furthermore, we establish correspondences between our notions and those already present in the literature, derive optimality bounds for the Mean-Field - $N$-player transition, and empirically demonstrate the convergence of these algorithms on simple games.

cs.GT↗

arXiv2022

Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.

cs.AI↗

arXiv2021

Statistical discrimination in learning agents

Undesired bias afflicts both human and algorithmic decision making, and may be especially prevalent when information processing trade-offs incentivize the use of heuristics. One primary example is \textit{statistical discrimination} -- selecting social partners based not on their underlying attributes, but on readily perceptible characteristics that covary with their suitability for the task at hand. We present a theoretical model to examine how information processing influences statistical discrimination and test its predictions using multi-agent reinforcement learning with various agent architectures in a partner choice-based social dilemma. As predicted, statistical discrimination emerges in agent policies as a function of both the bias in the training population and of agent architecture. All agents showed substantial statistical discrimination, defaulting to using the readily available correlates instead of the outcome relevant features. We show that less discrimination emerges with agents that use recurrent neural networks, and when their training environment has less bias. However, all agent algorithms we tried still exhibited substantial bias after learning in biased training populations.

cs.LG↗

arXiv2021

Evolutionary Dynamics and $Φ$-Regret Minimization in Games

Regret has been established as a foundational concept in online learning, and likewise has important applications in the analysis of learning dynamics in games. Regret quantifies the difference between a learner's performance against a baseline in hindsight. It is well-known that regret-minimizing algorithms converge to certain classes of equilibria in games; however, traditional forms of regret used in game theory predominantly consider baselines that permit deviations to deterministic actions or strategies. In this paper, we revisit our understanding of regret from the perspective of deviations over partitions of the full \emph{mixed} strategy space (i.e., probability distributions over pure strategies), under the lens of the previously-established $Φ$-regret framework, which provides a continuum of stronger regret measures. Importantly, $Φ$-regret enables learning agents to consider deviations from and to mixed strategies, generalizing several existing notions of regret such as external, internal, and swap regret, and thus broadening the insights gained from regret-based analysis of learning algorithms. We prove here that the well-studied evolutionary learning algorithm of replicator dynamics (RD) seamlessly minimizes the strongest possible form of $Φ$-regret in generic $2 \times 2$ games, without any modification of the underlying algorithm itself. We subsequently conduct experiments validating our theoretical results in a suite of 144 $2 \times 2$ games wherein RD exhibits a diverse set of behaviors. We conclude by providing empirical evidence of $Φ$-regret minimization by RD in some larger games, hinting at further opportunity for $Φ$-regret based study of such algorithms from both a theoretical and empirical perspective.

cs.GT↗

arXiv2021

Time-series Imputation of Temporally-occluded Multiagent Trajectories

In multiagent environments, several decision-making individuals interact while adhering to the dynamics constraints imposed by the environment. These interactions, combined with the potential stochasticity of the agents' decision-making processes, make such systems complex and interesting to study from a dynamical perspective. Significant research has been conducted on learning models for forward-direction estimation of agent behaviors, for example, pedestrian predictions used for collision-avoidance in self-driving cars. However, in many settings, only sporadic observations of agents may be available in a given trajectory sequence. For instance, in football, subsets of players may come in and out of view of broadcast video footage, while unobserved players continue to interact off-screen. In this paper, we study the problem of multiagent time-series imputation, where available past and future observations of subsets of agents are used to estimate missing observations for other agents. Our approach, called the Graph Imputer, uses forward- and backward-information in combination with graph networks and variational autoencoders to enable learning of a distribution of imputed trajectories. We evaluate our approach on a dataset of football matches, using a projective camera module to train and evaluate our model for the off-screen player state estimation setting. We illustrate that our method outperforms several state-of-the-art approaches, including those hand-crafted for football.

cs.LG↗